Schlumberger Limited (SLB) 8-K Schlumberger Announces the Offering of Senior Convertible Debentures

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of

the Securities Exchange Act of 1934

Date of Report (date of earliest event reported): June 3, 2003

SCHLUMBERGER N.V. (SCHLUMBERGER LIMITED)

(Exact name of registrant as specified in its charter)

Netherlands Antilles	1-4601	52-0684746
(State or other jurisdiction of incorporation)	(Commission File Number)	(IRS Employer Identification No.)

153 East 53rd Street, 57th Floor
New York, New York	10022-4624
42, rue Saint-Dominique
Paris, France	75007
Parkstraat 83,
The Hague,
The Netherlands	2514 JG
(Addresses of principal executive offices)	(Zip or Postal Codes)

Registrant’s telephone number in the United States, including area code: (212) 350-9400

Item 5.

Attached hereto as Exhibit 99.1 and incorporated by reference herein is the June 3, 2003 Schlumberger Limited press release.

Item 7.    FINANCIAL STATEMENTS AND EXHIBITS

(c )  Exhibits

99.1 June 3, 2003 Schlumberger Limited press release.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

SCHLUMBERGER N.V.
(SCHLUMBERGER LIMITED)
By:	/S/    FRANK A. SORGIE
	Frank A. Sorgie
	Chief Accounting Officer

Date: June 3, 2003